Do you need to know valve position other than when it hits max or min open? Or do you really need to know a process variable, such as flow?
I have hundreds of valves on systems controlling flow without valve position feedback. I used to just use limit switches at max (usually set to about 70%) and min (usually set to about 15%). I would simply tweak the valve until I got the flow I wanted. When the limit switch tripped I knew I was out of adjustment and had to do something else.
Tracking time is unlikely to be satisfactory. The gearing in the operator usually has clearances, so every time you move there will be some error. When reversing direction the error is greater. At some point the errors will accumulate enough to make your "position' useless.